Investigating Teachers' Mathematics Teaching Understanding: A Case for Coordinating Perspectives

This paper provides a microanalysis of one Algebra I teacher's instruction to explore the advantages that are afforded us by coordinating two perspectives to document and account for the teacher's mathematical understandings. We use constructs associated with Stein, Grover and Henningsen's domain of mathematical didactics and Realistic Mathematics Education's instructional design theory to infer what the teacher might understand to effectively implement her instructional goals and, more importantly, support student learning. By coordinating these perspectives, we developed a working framework for analyzing the teacher's classroom practice retrospectively. For example, we illustrate how the mathematical possibilities related to one student's question might inform the teacher's decisions as she initiates shifts in students' self-generated models. Additionally, we illustrate how the teacher's decision to capitalize on particular students' models contributes in part to the kinds of mathematical ideas that can be explored and the connections students can make among those ideas. More generally, we explore the utility of coordinating these two perspectives to understand the landscape of ideas that teachers might traverse to align their practices with reform recommendations in the United States.     

幸福,是个抉择

If it'S possible to see red(火冒三丈)about not seeing red,that is what Iwas doing.We had misjudged(错误判断,错误估计)the timing of our autumntrip to see the changing leaves in the Great Lakes states,and I was reallyupset.No matter how I strained my eyes,I couldn't spot red anywhere.NOteven a hint of golden yellow broke through the monotonous greenery. I recalled an earlier leaf-viewing trip to Vermont in October,and the     

Expanding and sustaining arts-based educational research as practitioner inquiry

ABSTRACT

As practitioner inquiry is now established as a widely-recognized research tradition and flourishing movement for educational change, we might consider ways that practitioner inquiry could be conceptualized and executed to broaden implementation, deepen understanding, and sustain inquiry within teacher education. Arts-based research may be an ideal methodology for the extension and sustainment of such inquiry as its visual, performative orientation lends itself to participant engagement and provides access in the representation and dissemination of results. This article will put forth models for advancing arts-based practitioner inquiry within the field of teacher education, by drawing from multiple cycles of a dual-layered, ABER study. This vision of arts-based practitioner inquiry is that of inclusion, increasing the number of those who conduct and interact with research; collaboration, blurring boundaries between the inquiries of teacher educators and pre-service teachers; accessibility, tapping into the power of the arts to engage and communicate in ways that scientific language cannot; and continued engagement, using learning from one cycle to inform inquiry in the next.     

Academic Trajectories of Children in Formal and Informal Kinship Care

The academic achievement places children on a positive trajectory for their lifespan. The aim of this study was to examine the academic trajectories of children in out-of-home care (OOCH) and whether kinship care has a protective effect relative to nonkin foster care. The sample analyzed for this study consists of 519,306 racially diverse youth in North Carolina schools 8 to 11 years old in the school year 2009–2010 (e.g., 27% African American, 12% Latinx, 53% White). Four longitudinal administrative data sources were merged to create this unique sample. Multilevel modeling revealed no difference between formal and non-OOHC, but showed differences between nonkin foster, informal, and non-OOHC. Children’s academic performance who reside in formal kinship care is similar to children in non-OOHC.     

High school science enrollment of black students

How can the high school science enrollment of black students be increased? School and home counseling and classroom procedures could benefit from variables identified as predictors of science enrollment. The problem in this study was to identify a set of variables which characterize science course enrollment by black secondary students. The population consisted of a subsample of 3963 black high school seniors from The High School and Beyond 1980 Base-Year Survey. Using multiple linear regression, backward regression, and correlation analyses, the US Census regions and grades mostly As and Bs in English were found to be significant predictors of the number of science courses scheduled by black seniors.     

Memoir as a form of auto-ethnographic research for exploring the practice of transnational higher education in China

In this paper, I argue that memoir, as a form of auto-ethnographic research, is an appropriate method for exploring the complexities and singularities in the practice of western educational practitioners who are immersed in the social reality of offshore higher education institutions, such as those in Mainland China. I illustrate this proposition by showing how my own use of memoir is guided by a need to interrogate the unique experiences of my past life as ‘the foreigner’, ‘the special one’, ‘the imported expert’ and ‘the cultural outsider’, in order to lay bare the complexity of what it means to work and live in China as a foreign teacher and be recognised as different. I am interested in the notion of foreignness, and the ambiguities that arise when one operates as a teacher in a foreign culture, with a misguided and naïve understanding of one's own specialness as the foreign expert. My research methodology is based on critically reflective writing that acknowledges the multiplicity of historical, cultural and social differences, and the uniqueness of all individuals, whilst recognising that difference, at its heart, is a matter of relationship(s). This form of writing as educational research makes it possible to challenge some of the generalisations western scholars inadvertently make when writing about their teaching experiences in China.     

Documenting support needs and adjustment gaps for students with disabilities: teacher practices in Australian classrooms and on national tests

Accommodations or adjustments for students with disabilities (SWDs) who need them are required in Australian education law and policy for classroom instruction and assessment, and external educational accountability tests. Drawing upon the structure of the Assessment Accommodations Checklist and more than a decade of accessibility research, the Checklist of Learning and Assessment Adjustments for Students (CLAAS) was developed to help teachers select and document adjustments that support SWDs and students with additional needs in classroom instruction and assessment, and external tests. The CLAAS was trialled with 21 primary school teachers documenting adjustments for 89 students with diverse needs. Teachers indicated that the CLAAS provided a comprehensive list of adjustments, was useful for recording adjustments across classroom instruction and assessment, and external tests, and provided guidance about potential adjustments for SWDs or with additional learning needs. The documented adjustments also indicated some considerable gaps between supports provided in classrooms compared with the Australian educational accountability tests. Findings also provided initial evidence for the reliability and validity of use of the CLAAS for its intended purposes. The CLAAS is a promising tool for helping both researchers and teachers systematically document and provide equitable and inclusive adjustments for SWDs and additional learning needs given their needs for classroom learning, assessment and external testing and examination requirements.     

Enhanced use of educational accountability data to monitor educational progress of Australian students with focus on Indigenous students

Educational Assessment, Evaluation and Accountability - In Australia, under the National Assessment Plan, educational accountability testing in literacy and numeracy (NAPLAN) is undertaken with all...     

Attitudes towards Innovations in Primary Schools: A Study of In-Service Teachers

This is a study of how a group of primary school teachers in Singapore dealt with the possibility of introducing informal educational innovations in their school settings. “Informal innovations” here refers to the voluntary adoption of new teaching methods, techniques and ideas acquired during an in-service teacher education programme, namely, the Further Professional Certificate in Education (FPCE) programme conducted by the Institute of Education, Singapore. Did these teachers attempt, when back in their schools, to experiment with the new ideas and methods of teaching they had been exposed to during the one year of the FPCE programme? What factors worked for, and against, attempts at innovations in their primary schools? Were there structural constraints and socio-psychological obstacles that they had to negotiate in order to adopt innovations in classroom and educational practices? If innovative ideas had remained dormant, was this because the teachers were unconvinced about the practicality and relevance of these ideas for the classroom and the school? These questions serve as the focal points of a small study involving 66 primary school teachers. Of the 66 teachers, sixteen had resumed work at school for nine months after they completed their in-service attachment at the Institute of Education (IE). The remaining 50 were in the midst of their in-service training when they participated in the study.